For parallelograms,it looks like AA' and CC' define the same line asdo BB' and DD'. For all other quadrilaterals (convex, concave, even reflex) the four linesare concurrent. Note that for some quadrilaterals,X = X' and we only have three lines. But, the threelines are concurrent.

So maybe instead of saying that the four linesare concurrent, we should say the "four" linespass through the same point.